The classification of complete stable area-stationary surfaces in the Heisenberg group
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Publication:968817
DOI10.1016/j.aim.2009.12.002zbMath1192.53038arXiv0810.5249OpenAlexW2057243284MaRDI QIDQ968817
Ana Hurtado, César Rosales, Manuel Ritoré
Publication date: 10 May 2010
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0810.5249
second variationHeisenberg groupssingular setsarea-minimizing surfacesstable area-stationary surfaces
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Cites Work
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- An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
- Existence and uniqueness for \(p\)-area minimizers in the Heisenberg group
- Regular submanifolds, graphs and area formula in Heisenberg groups
- Constant mean curvature surfaces in sub-Riemannian geometry
- Area-stationary surfaces in the Heisenberg group \(\mathbb H^1\)
- Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group \(\mathbb H^1\)
- Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group \({\mathbb{H}^1}\) with low regularity
- On complete minimal surfaces with finite Morse index in three manifolds
- Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
- Sub-Riemannian calculus on hypersurfaces in Carnot groups
- One-sided complete stable minimal surfaces
- Area-stationary surfaces inside the sub-Riemannian three-sphere
- Metric normal and distance function in the Heisenberg group
- \(H\)-minimal graphs of low regularity in \(\mathbb H^1\)
- Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group \(\mathbb H^n\)
- The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
- Properly embedded and immersed minimal surfaces in the Heisenberg group
- A notable family of entire intrinsic minimal graphs in the Heisenberg group which are not perimeter minimizing
- The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
- Stable complete minimal surfaces in 𝑅³ are planes
- Size of characteristic sets and functions with prescribed gradient
- Riemannian geometry of contact and symplectic manifolds
- Sur un théorème de traces. (On a trace theorem)
- Rectifiability and perimeter in the Heisenberg group
- Surface measures in Carnot-Carathéodory spaces
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